The Author commences by stating that he has in the course of his investigations found the theory of probabilities in a far from perfect state. In many cases, when he has wished to make use of the theory of probabilities, he has searched in vain for demonstrated formulae capable of immediate application, and he has generally been obliged to begin by working out the formulae independently for himself.

At the present time the subject of legislation in reference to Insurance Companies is attracting much attention in Germany as well as England. Until quite recently the regulation of insurance matters in Germany was under the sole control of the several States, as is still the case in the United States of America: the former German Confederation possessing neither the organization nor the authority to interfere in the matter. As a consequence of this state of affairs, we are informed that a company organized in one of the German States was regarded in the others as a foreign company, and all companies, whether German or foreign, which desired to extend their business over the whole of Germany, were compelled to put themselves in communication with more than thirty different Governments, each of which had its own special regulations. Some of the larger States had passed laws on the subject, but the provisions of them differed very widely from each other. In the remaining States, each Government imposed on the companies such conditions as it thought proper. This state of things is evidently very unfavourable for Insurance Companies, which require—more than any other undertaking—a wide field for their successful development. Under the old political organization of Germany, a uniform system of legislation, though long and ardently desired, was quite unattainable. But after the events of the year 1866 had led to the formation of the present North German Confederation, which gives a common legislation to at least three-fourths of Germany, the hopes of reformers revived. The 4th article of the Constitution of the Confederation expressly provides that legislation upon insurance shall belong to the province of the Confederation.